# ch12 - Chapter 12 Instrumental Variables Regression...

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Unformatted text preview: Chapter 12 Instrumental Variables Regression Instrumental Variables Regression Recall the least square assumption #1: The error term u i has conditional mean zero given X i : E ( u i j X i ) = 0. When the regressor X is correlated with the error term, the assumption is violated. I If corr ( X i , u i ) 6 = 0, E ( u i j X i ) must be nonzero. Instrumental variables (IV) regression solves this problem. The IV Model and Assumptions Consider the population regression model Y i = β + β 1 X i + u i , i = 1, ..., n , If u i and X i are correlated, the OLS estimator is inconsistent. IV estimation uses an additional instrumental variable (or simply instrument) Z to isolate the part of X that is uncorrelated with u i . The IV Model and Assumptions Endogeneity and exogeneity: I Endogenous variables : Variables correlated with the error term I Exogenous variables : Variables uncorrelated with the error term A valid instrumental variable must satisfy two conditions: 1. Instrument relevance : corr ( Z i , X i ) 6 = 0....
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ch12 - Chapter 12 Instrumental Variables Regression...

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